The measure of an angle is an arc of any circle contained between the two lines which form that angle, the angular point being the centre; and it is estimated by the number of degrees contained in that arc. Hence a right angle being measured by a quadrant, or quarter of a circle, is an angle of 90 degrees. The sum of the three angles of every triangle is equal to 180 degrees, or two right angles; therefore, in a right-angled triangle, taking one of the acute angles from 90 degrees, leaves the other acute angle; and the sum of the two angles in any triangle, taken from 180 degrees, leaves the third angle; or one angle being taken from 180 degrees leaves the sum of the other two angles.
Definitions.
The sine of an arc is the line drawn from one extremity of the arc perpendicular to the diameter of the circle which passes through the other extremity.
The supplement of an arc is the difference, in degrees, between the arc, and a semicircle, or 180 degrees.
The complement of an arc is the difference, in degrees, between the arc, and a quadrant, or 90 degrees.
The tangent of an arc is a line touching the circle in one extremity of that arc, continued from thence to meet a line drawn from the centre through the other extremity; which last line is called the secant of the same arc.
The cosine, cotangent, and cosecant of an arc are the sine, tangent, and secant of the complement of that arc, the co being only a contraction of the word complement.
The sine, tangent, or secant of an angle is the sine, tangent, or secant of the arc by which the angle is measured, or of the degrees, &c., in the same arc, or angle. Vide also [Definitions], Practical Geometry.
There are two Methods of resolving triangles, or the cases of trigonometry—viz., Construction, and Computation.
1st method.—The triangle is constructed by making the sides from a scale of equal parts, and laying down the angles from the protractor. Then, by measuring the unknown parts by the same scale, the solution will be obtained.